A113670 Self-convolution 4th power equals A113664, where a(n) = n*A113664(n-1) for n>=1, with a(0)=1.

1, 1, 8, 114, 2224, 53725, 1528200, 49703108, 1813503712, 73247619060, 3242579748000, 156107189374202, 8121266448765936, 454110696002834806, 27165980379205109232, 1731608155057922555400, 117183510733473232477120

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

G.f. A(x) satisfies:

(1) A(x) = 1 + x*d/dx[x*A(x)^4],

(2) [x^n] exp( x*A(x)^4 ) * (n + 1 - A(x)) = 0 for n > 0,

(3) [x^n] exp( n * x*A(x)^4 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A^4)); polcoeff(A, n, x)}

Crossrefs

Cf. A113664, A000699, A113669, A113671, A113672, A113673, A113674.

Sequence in context: A062126 A222520 A220635 * A347019 A156468 A293992

Adjacent sequences: A113667 A113668 A113669 * A113671 A113672 A113673

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2005

Status

approved